# What is the equation of the line perpendicular to y=27/12x  that passes through  (2,1) ?

Mar 3, 2018

suppose,the equation of the line required is $y = m x + c$

Now,slope of the given equation $y = \left(\frac{27}{12}\right) x$ is $\frac{27}{12} = \frac{9}{4}$

If, our required straight line needs to be perpendicular on the given staright line,then we can say, $m . \left(\frac{9}{4}\right) = - 1$

So, $m = - \left(\frac{4}{9}\right)$

So,we found the slope of our line,hence we can put it and write as,

$y = \frac{- 4 x}{9} + c$

Now,given that this line passes through the point $\left(2 , 1\right)$

So,we can put the value to determine the intercept,

so, $1 = \frac{- 4 \cdot 2}{9} + c$

or, $c = \frac{17}{9}$

So,the equation of our line becomes, $y = \frac{- 4 x}{9} + \frac{17}{9}$ or, $9 y + 4 x = 17 g r a p h \left\{9 y + 4 x = 17 \left[- 10 , 10 , - 5 , 5\right]\right\}$